Dangers of Statistical Illiteracy
Voter fraud statistics and AP class difficulty: what do these two have in common?
You watch the news one day and hear that voter fraud is such a huge issue as there are hundreds of instances. Your friend somewhere says that AP Environmental Science is such a difficult course and that BC calculus is the easiest math course because of the distributions of 5s. How many claims, not just these, are true? Are votes actually being swung by illegal voters? Is Calc BC a very easy class?
From the entire year of 2024, Heritage Database, reported 43 instances of people convicted of voter fraud. This included all categories. According to the United States Census Bureau, 154 million people voted. This number is rounded as there are very small chances that it is exactly 154 million. The number is rounded to the nearest million so expect some numbers to be off. Now, we can now do some simple statistics to find the percent of voter fraud.
Which results to 0.0000279220779221%. That is a very small number. If I were to allow all instances of voter fraud from 1982 to 2025, there are 1620 instances of voter fraud. This does seem bad, thousands of votes are fabricated but now we have to realize the entire sample. 1982-2025. In a single year presidential election, there were 154,000,000 votes.
Even if we were to place 1620/154,000,000
we would receive 0.00105194805195% which is still really small. This is excluding all the years except 2024. According to the United States Census Bureau, in 2020 there were 154.6 million voters, in 2016, there were 137.5 million and so on.
America is a country with a lot of problems, but the simplest of statistics show that voter fraud has such a slight effect in America that it is almost negligible. For example, if you were to have 154 million dollars in your bank account, and if you suddenly lost 43 dollars, you’d be a little sad and simply withdraw another 43 dollars from your bank account. By simply analyzing the numbers, you can come up with much more reasonable and accurate conclusions.
Hypothetically, if I was an unaware student who simply looked at the percentage of students who got a 5 on the BC exam, I’d be inclined to take the course. In fact, in a short interview with Landon Smith, he agreed based on the statistics showing the high pass rate.
Year in and year out, the College board reports around 40% of students who take the BC calculus exam get a 5, making it seem like a super easy course. However, we have failed to meet one of the checks for inference. The sample is not representative of the population. (If you’re interested in learning more about the checks for inference simply read the AP statistics textbook found in the library or take AP Stats). The students who take BC are hardened math warriors who did well on the AB exam. Objectively, BC is way more complicated than AB, but students do better since the average student in BC got a 5 on AB.
In contrast to AP Environmental Science, where there are no pre-requisite gateways such as Calc AB, everyone can take this course. The College Board reports around 8-10% of students get a 5. On paper, this seems much more intimidating than Calc BC, but the sample this time is any student, including seniors who don’t care and students who can’t read. APES is more of the typical AP course, not particularly hard nor easy, just distribution is disturbed by other variables (Lurking Variables for AP Stats takers) instead of difficulty.
Typically any numerical statement is true. There is definitely voter fraud. Getting 5 on the BC exam is very common; however, it is more important to consider the context. In a situation where hundreds of millions of people vote, is missing even 100 votes a big problem that should be fixated on? There are bigger problems to tackle, such as the national debt, global conflict, educational reform and other such things. When a population is misled by numbers, it is easy to get off track from the larger problems in society.
Statistics is used to realize the true meaning of numbers. It is important to learn them so that informed choices are made. That said, for those people who want to challenge BC suffering, have fun.
